Abstract

Analytic properties of the Jost function in g, the coupling constant, are studied for potentials which are L½, i.e., , and have a negative power or exponential tail for large distances. For the bound state and scattering problems, it is found that the Jost function has exponential order ½ for large g, which implies that the scattering phase shift and the number of bound states in an attractive potential grow like |g|½ for large g. The latter result is the best possible and is a considerable improvement over earlier estimates.